I would like to leverage an existing (and patented) research methodology, but use it in a different way. The current patented methodology relies on a specific process of humans prescribing assignments and asking questions of other humans, whereas I believe that this process could be conducted in a different way online (in mass quantity) and become more scalable and more accurate.

I want to give credit and recognition to the original patent holder. I'm just wondering how much say they will/should have in the deployment of a modified process that takes their original concept to the next level, and how much it will likely cost to leverage their original invention.

This is a good answer. Even if you believe that you are avoiding their claims, they can still sue you. Once in front of a lay jury, you can lose even if you are right. Some organizations get a freedom to operate opinion from a qualified external attorney. This can help in fighting a suit and if you end up losing a suit it may help in avoiding punitive awards.
– Eric ShainDec 26 '16 at 15:38